Local Principal Component Analysis Research Articles

AN EFFICIENT METHOD FOR AUTOMATIC ROAD EXTRACTION BASED ON MULTIPLE FEATURES FROM LiDAR DATA

The road extraction in urban areas is difficult task due to the complicated patterns and many contextual objects. LiDAR data directly provides three dimensional (3D) points with less occlusions and smaller shadows. The elevation information and surface roughness are distinguishing features to separate roads. However, LiDAR data has some disadvantages are not beneficial to object extraction, such as the irregular distribution of point clouds and lack of clear edges of roads. For these problems, this paper proposes an automatic road centerlines extraction method which has three major steps: (1) road center point detection based on multiple feature spatial clustering for separating road points from ground points, (2) local principal component analysis with least squares fitting for extracting the primitives of road centerlines, and (3) hierarchical grouping for connecting primitives into complete roads network. Compared with MTH (consist of Mean shift algorithm, Tensor voting, and Hough transform) proposed in our previous article, this method greatly reduced the computational cost. To evaluate the proposed method, the Vaihingen data set, a benchmark testing data provided by ISPRS for “Urban Classification and 3D Building Reconstruction” project, was selected. The experimental results show that our method achieve the same performance by less time in road extraction using LiDAR data.

AN EFFICIENT METHOD FOR AUTOMATIC ROAD EXTRACTION BASED ON MULTIPLE FEATURES FROM LiDAR DATA

Abstract. The road extraction in urban areas is difficult task due to the complicated patterns and many contextual objects. LiDAR data directly provides three dimensional (3D) points with less occlusions and smaller shadows. The elevation information and surface roughness are distinguishing features to separate roads. However, LiDAR data has some disadvantages are not beneficial to object extraction, such as the irregular distribution of point clouds and lack of clear edges of roads. For these problems, this paper proposes an automatic road centerlines extraction method which has three major steps: (1) road center point detection based on multiple feature spatial clustering for separating road points from ground points, (2) local principal component analysis with least squares fitting for extracting the primitives of road centerlines, and (3) hierarchical grouping for connecting primitives into complete roads network. Compared with MTH (consist of Mean shift algorithm, Tensor voting, and Hough transform) proposed in our previous article, this method greatly reduced the computational cost. To evaluate the proposed method, the Vaihingen data set, a benchmark testing data provided by ISPRS for “Urban Classification and 3D Building Reconstruction” project, was selected. The experimental results show that our method achieve the same performance by less time in road extraction using LiDAR data.

Single Image Face Recognition based on Gabor, Sobel and Local Ternary Pattern

Face recognition has been a fast growing, challenging and fascinating area in real time applications. A large number of face recognition algorithms have been developed in last decades. This paper presents a face recognition approach that utilizes the Sobel operator, Local Ternary Pattern (LTP) descriptor, Gabor features and Principal Component Analysis (PCA) algorithms to attain enhanced recognition accuracy where training set has only one image per person. In particular, the edge information of face image is enhanced using Sobel operator. Then we use LTP on the image to encode the micro-level information of spots, edges and other local characteristics. Finally Gabor-wavelets based features are then extracted and their histograms are concatenated together into a contiguous histogram to be used as a descriptor of the face. As Gabor features cause a very high dimensional histogram vector, therefore PCA is used to reduce the dimension. This approach is compared with the original LBP, LTP and Sobel LTP on gray-level images for face recognition. The experimental results exhibit that our method provides a remarkable performance under various conditions.

Understanding machine‐learned density functionals

Machine learning (ML) is an increasingly popular statistical tool for analyzing either measured or calculated data sets. Here, we explore its application to a well‐defined physics problem, investigating issues of how the underlying physics is handled by ML, and how self‐consistent solutions can be found by limiting the domain in which ML is applied. The particular problem is how to find accurate approximate density functionals for the kinetic energy (KE) of noninteracting electrons. Kernel ridge regression is used to approximate the KE of non‐interacting fermions in a one dimensional box as a functional of their density. The properties of different kernels and methods of cross‐validation are explored, reproducing the physics faithfully in some cases, but not others. We also address how self‐consistency can be achieved with information on only a limited electronic density domain. Accurate constrained optimal densities are found via a modified Euler‐Lagrange constrained minimization of the machine‐learned total energy, despite the poor quality of its functional derivative. A projected gradient descent algorithm is derived using local principal component analysis. Additionally, a sparse grid representation of the density can be used without degrading the performance of the methods. The implications for machine‐learned density functional approximations are discussed. © 2015 Wiley Periodicals, Inc.

GMM and optimal principal components-based Bayesian method for multimode fault diagnosis

Principal component analysis (PCA) serves as the most fundamental technique in multivariate statistical process monitoring. However, other than determining contributions to a fault from each variable based on the pre-selected major principal components (PCs), the PCA-based fault diagnosis with an optimal selection of PCs is seldom investigated. This paper presents a novel Gaussian mixture model (GMM) and optimal principal components (OPCs)-based Bayesian method for efficient multimode fault diagnosis. First, the GMM and Bayesian inference is utilized to identify the operating mode, and then local PCA model is established in each mode. Second, given that the various principal components (PCs) may contain distinct fault signatures, the behavior of each PC in local PCA is examined and the OPCs are selected through stochastic optimization algorithm. Based on the OPCs, a Bayesian diagnosis system is then formulated to identify the fault statuses in a probability manner. Performance of GMM–OPC Bayesian diagnosis is examined through a numerical example and the Tennessee Eastman challenge process. The efficiency and feasibility are demonstrated.

Building spatial composite indicators to analyze environmental health inequalities on a regional scale.

BackgroundReducing health inequalities involves the identification and characterization of social and exposure factors and the way they accumulate in a given area. The areas of accumulation then allow for prioritization of interventions. The present study aims to build spatial composite indicators based on the aggregation of environmental, social and health indicators and their inter-relationships.MethodPreliminary work was carried out firstly to homogenize spatial coverage, and secondly to study spatial variation of environmental (EI), socioeconomic (SI) and health (HI) indicators. The aggregation of the different indicators was performed using several methodologies for which results and decision-makers’ usability were compared.ResultsFour methodologies were tested: 1) A simple summation of normalized HI, EI and SI indicators (IC), 2) the sum of the normalized HI, EI and SI indicators weighted by the first principal component of a Principal Component Analysis (IC PCA), 3) the sum of normalized and weighted indicators of the first principal component of Local Principal Component Analysis (IC LPCA), and 4) the sum of normalized and weighted indicators of the first principal component of a Geographically Weighted Principal Component Analysis (IC GWPCA).ConclusionThe GWPCA is particularly adapted to taking into account the spatial heterogeneity and the spatial autocorrelation between SI, EI and HI. This approach invalidates the basic assumptions of many standard statistical analyses. Where socioeconomic indicators present high deprivation and where they are associated with potential modifiable health determinants, decision-makers can prioritize these areas for reducing inequalities by controlling the socioeconomic and health determinants.

Semisupervised Support Vector Machines With Tangent Space Intrinsic Manifold Regularization.

Semisupervised learning has been an active research topic in machine learning and data mining. One main reason is that labeling examples is expensive and time-consuming, while there are large numbers of unlabeled examples available in many practical problems. So far, Laplacian regularization has been widely used in semisupervised learning. In this paper, we propose a new regularization method called tangent space intrinsic manifold regularization. It is intrinsic to data manifold and favors linear functions on the manifold. Fundamental elements involved in the formulation of the regularization are local tangent space representations, which are estimated by local principal component analysis, and the connections that relate adjacent tangent spaces. Simultaneously, we explore its application to semisupervised classification and propose two new learning algorithms called tangent space intrinsic manifold regularized support vector machines (TiSVMs) and tangent space intrinsic manifold regularized twin SVMs (TiTSVMs). They effectively integrate the tangent space intrinsic manifold regularization consideration. The optimization of TiSVMs can be solved by a standard quadratic programming, while the optimization of TiTSVMs can be solved by a pair of standard quadratic programmings. The experimental results of semisupervised classification problems show the effectiveness of the proposed semisupervised learning algorithms.

Localized Functional Principal Component Analysis

We propose localized functional principal component analysis (LFPCA), looking for orthogonal basis functions with localized support regions that explain most of the variability of a random process. The LFPCA is formulated as a convex optimization problem through a novel deflated Fantope localization method and is implemented through an efficient algorithm to obtain the global optimum. We prove that the proposed LFPCA converges to the original functional principal component analysis (FPCA) when the tuning parameters are chosen appropriately. Simulation shows that the proposed LFPCA with tuning parameters chosen by cross-validation can almost perfectly recover the true eigenfunctions and significantly improve the estimation accuracy when the eigenfunctions are truly supported on some subdomains. In the scenario that the original eigenfunctions are not localized, the proposed LFPCA also serves as a nice tool in finding orthogonal basis functions that balance between interpretability and the capability of explaining variability of the data. The analyses of a country mortality data reveal interesting features that cannot be found by standard FPCA methods. Supplementary materials for this article are available online.

Feature Extraction for Facial Expression Recognition based on Ensemble Learning Algorithm

The accuracy of facial expression feature extraction directly influences the recognition rate of facial expression. In order to extract facial expression feature effectively, this paper puts forward a new way of facial expression feature extraction ensemble learning algorithm based on ensemble thinking. The superposition method of heteromorphy ensemble learning is used to construct an ensemble learning model, two-d gabor wavelet, block local binary patterns and two-directional two-dimensional principal component analysis as the single learning device. Firstly, two-d gabor wavelet was used to get image texture information at each level. Then the image was divided into some blocks to acquire the eigenvectors of block local binary patterns, and reduced its dimensionality. Next, the dimensionality was further reduced by two-directional two-dimensional principal component analysis, extracted the effective characteristic features at the same time. Finally, it is classified by nearest neighbor classifier on the extracted feature library. Experimental results on JAFFE expression database show that this ensemble learning model gets higher recognition rate and better generalization ability than single learning device.

Nonlinear gradient denoising: Finding accurate extrema from inaccurate functional derivatives

A method for nonlinear optimization with machine learning (ML) models, called nonlinear gradient denoising (NLGD), is developed, and applied with ML approximations to the kinetic energy density functional in an orbital‐free density functional theory. Due to systematically inaccurate gradients of ML models, in particular when the data is very high‐dimensional, the optimization must be constrained to the data manifold. We use nonlinear kernel principal component analysis (PCA) to locally reconstruct the manifold, enabling a projected gradient descent along it. A thorough analysis of the method is given via a simple model, designed to clarify the concepts presented. Additionally, NLGD is compared with the local PCA method used in previous work. Our method is shown to be superior in cases when the data manifold is highly nonlinear and high dimensional. Further applications of the method in both density functional theory and ML are discussed. © 2015 Wiley Periodicals, Inc.

MRI noise estimation and denoising using non-local PCA.

This paper proposes a novel method for MRI denoising that exploits both the sparseness and self-similarity properties of the MR images. The proposed method is a two-stage approach that first filters the noisy image using a non local PCA thresholding strategy by automatically estimating the local noise level present in the image and second uses this filtered image as a guide image within a rotationally invariant non-local means filter. The proposed method internally estimates the amount of local noise presents in the images that enables applying it automatically to images with spatially varying noise levels and also corrects the Rician noise induced bias locally. The proposed approach has been compared with related state-of-the-art methods showing competitive results in all the studied cases.

Field-Based near Infrared Spectroscopy for Analysis of Scandinavian Stone Age Rock Paintings

During the early autumn of 2014 a field-based near infrared (NIR) spectroscopy study was carried out at Swedish and Norwegian Stone Age rock painting sites. This article presents results from one of them, namely Flatruet, Härjedalen, Sweden. Here, field-based NIR measurements were conducted using the 908–1676 nm wavelength range to gather 479 spectra: 427 of rock paintings and 52 of local lithology background. The whole dataset was analysed using principal component analysis (PCA) and four principal components were extracted explaining 98.5% (PC1), 1.4% (PC2), 0.06% (PC3) and 0.04% (PC4). The PCA results showed that there was a large spread in the spectra of both background and red paint objects, but also some evidence of clustering could be seen where background and paintings could be separated. An improvement in separation was achieved with partial least squares discriminant analysis (PLS-DA) using the background and paint as categorical variables. The most important components of the PLS-DA model showed a better separation in the score plot. A small test set of 10 paint and 10 background samples showed that one of the paint samples and two of the background samples were misclassified. One conclusion is that there is a large spread in background due to varying precipitation of secondary iron oxides. It was also decided to look deeper into local models of painted elks and their pigments alone. This was done using local PCA models and soft independent modelling of class analogies showing that some painted elks could be separated from each other while others were quite similar, which is important for answering questions about origin, age and weathering.

Enhancements to a Geographically Weighted Principal Component Analysis in the Context of an Application to an Environmental Data Set

In many physical geography settings, principal component analysis (PCA) is applied without consideration for important spatial effects, and in doing so, tends to provide an incomplete understanding of a given process. In such circumstances, a spatial adaptation of PCA can be adopted, and to this end, this study focuses on the use of geographically weighted principal component analysis (GWPCA). GWPCA is a localized version of PCA that is an appropriate exploratory tool when a need exists to investigate for a certain spatial heterogeneity in the structure of a multivariate data set. This study provides enhancements to GWPCA with respect to: (i) finding the scale at which each localized PCA should operate; and (ii) visualizing the copious amounts of output that result from its application. An extension of GWPCA is also proposed, where it is used to detect multivariate spatial outliers. These advancements in GWPCA are demonstrated using an environmental freshwater chemistry data set, where a commentary on the use of preprocessed (transformed and standardized) data is also presented. The study is structured as follows: (1) the GWPCA methodology; (2) a description of the case study data; (3) the GWPCA application, demonstrating the value of the proposed advancements; and (4) conclusions. Most GWPCA functions have been incorporated within the GWmodel R package.

Leukemia and small round blue-cell tumor cancer detection using microarray gene expression data set: Combining data dimension reduction and variable selection technique

Using gene expression data in cancer classification plays an important role for solving the fundamental problems relating to cancer diagnosis. Because of high throughput of gene expression data for healthy and patient samples, a variable selection method can be applied to reduce complexity of the model and improve the classification performance. Since variable selection procedures pose a risk of over-fitting, when a large number of variables with respect to sample are used, we have proposed a method for coupling data dimension reduction and variable selection in the present study. This approach uses the concept of variable clustering for the original data set. Significant components of local principal component analysis models have just been retained from all clusters. Then, the variable selection algorithm is performed on these locally derived principal component variables. The proposed algorithm has been evaluated on two gene expression data sets; namely, acute Leukemia and small round blue-cell tumor (SRBCT). Our results confirmed that the classification models achieved on the reduced data were better than those obtained on the entire microarray gene expression profile.

Abstract 565: Genome-wide miRNA Expression Profiling and OPLS Discriminant Analysis in Hypertension and Cardiac Disease

MicroRNAs (miRNAs) are regulators of gene expression and play a key role in the pathophysiology of various disease processes, namely cardiovascular disease. This study aimed at the identification of the miRNA expression pattern of peripheral blood mononuclear cells derived from hypertensive subjects (HT) and non-hypertensive subjects with cardiac disease (CD) using a genome-wide approach. Furthermore, we explored the potential of orthogonal partial least squares-discrimination analysis (OPLS-DA) to analyze miRNA expression data. The homogeneity of the population was assessed with Principal Component Analysis (PCA) and verified by the clear separation of the three groups on the basis of the miRNA expression levels. Moreover, local PCA of HT group indicates the splitting of this group in two distinct subgroups. This distinction correlates with two subject’s characteristics (smoking habits and history of myocardial infarction) that are closest to the CD group. OPLS-DA analysis confirms the separation of three groups and identified the most important miRNA to discrimination between groups. Among the most influential miRNA to the positive differentiation of HT from CD and control, several of them are relevant to endothelial dysfunction. On the other hand, miRNAs associated with angiogenesis positively differentiate CD from HT and control. Mir-186, a regulator of myogenin, is the most important miRNA to discriminate HT from CD. These results provide evidence of altered miRNA profile in hypertensives and cardiac disease and demonstrate that PCA and OPLS-DA are very useful and robust tools to analyze how different miRNAs contribute to the separations of groups and to find interesting patterns within the multidimensional data.

Reduced-order PCA models for chemical reacting flows

One of the most challenging aspects of turbulent combustion research is the development of reduced-order combustion models which can accurately reproduce the physics of real systems. The identification and utilization of the low dimensional manifolds in these system is paramount to understand and develop robust models which can account for turbulence–chemistry interactions. Recently, principal components analysis (PCA) has been given notable attention in its analysis of reacting systems, and its potential in reducing the number of dimensions with minimum reconstruction error. The present work provides a methodology which has the ability of exploiting the information obtained from PCA. Two formulations of the approach are shown: Manifold Generated from PCA (MG-PCA), based on a global analysis, and Manifold Generated from Local PCA (MG-L-PCA), based on performing the PCA analysis locally. The models are created using the co-variance matrix of a data-set which is representative of the system of interest. The reduced models are then used as a predictive tool for the reacting system of interest by transporting only a subset of the original state-space variables on the computational grid and using the PCA basis to reconstruct the non-transported variables. The present study first looks into the optimal selection of the subset of transported variables and analyzes the effect of this selection on the approximation of the state space and chemical species source terms. Then, a demonstration of various a posteriori cases is presented.

Genome-wide association tests of inversions with application to psoriasis

Although inversions have occasionally been found to be associated with disease susceptibility through interrupting a gene or its regulatory region, or by increasing the risk for deleterious secondary rearrangements, no association study has been specifically conducted for risks associated with inversions, mainly because existing approaches to detecting and genotyping inversions do not readily scale to a large number of samples. Based on our recently proposed approach to identifying and genotyping inversions using principal components analysis (PCA), we herein develop a method of detecting association between inversions and disease in a genome-wide fashion. Our method uses genotype data for single nucleotide polymorphisms (SNPs), and is thus cost-efficient and computationally fast. For an inversion polymorphism, local PCA around the inversion region is performed to infer the inversion genotypes of all samples. For many inversions, we found that some of the SNPs inside an inversion region are fixed in the two lineages of different orientations and thus can serve as surrogate markers. Our method can be applied to case-control and quantitative trait association studies to identify inversions that may interrupt a gene or the connection between a gene and its regulatory agents. Our method also offers a new venue to identify inversions that are responsible for disease-causing secondary rearrangements. We illustrated our proposed approach to case-control data for psoriasis and identified novel associations with a few inversion polymorphisms.

Nonstationary multiscale turbulence simulation based on local PCA

Turbulence simulation methods are of fundamental importance for evaluating the performance of control strategies for Adaptive Optics (AO) systems. In order to obtain a reliable evaluation of the performance a statistically accurate turbulence simulation method has to be used. This work generalizes a previously proposed method for turbulence simulation based on the use of a multiscale stochastic model. The main contributions of this work are: first, a multiresolution local PCA representation is considered. In typical operating conditions, the computational load for turbulence simulation is reduced approximately by a factor of 4, with respect to the previously proposed method, by means of this PCA representation. Second, thanks to a different low resolution method, based on a moving average model, the wind velocity can be in any direction (not necessarily that of the spatial axes). Finally, this paper extends the simulation procedure to generate, if needed, turbulence samples by using a more general model than that of the frozen flow hypothesis.

Alternative c-Means基準を用いたロバストな局所的主成分分析による多次元データの２次元視覚化

Alternative c-Means基準を用いたロバストな局所的主成分分析による多次元データの２次元視覚化

Automatic Feature Extraction Using Replica Based Approach in Digital Fundus Images

In diabetic retinopathy, exudates play a major part which causes blindness to the diabetic patients. Diabetic patients lost its vision if the exudates will extend to the macular area of the retina. Spreading of this disease on the retina is prevented by automated early detection of presence of exudates. So, it is necessary to prevent the exudates which act as a major challenge in diagnostic task. The presence of exudates is identified based on the variation in grey color presents in retina. The recognition of the optic disc is necessary in the exudates detection procedure while both are related in terms of color, contrast, etc. A various techniques has studied before like morphological approach, region growing approach and so on for the detection of automatic diabetic retinopathy. But the automatic retinal detection leads to a greater chance of loss of sight if the detection is not done properly. So, to enhance the automatic feature extraction in digital fundus images, in this work, we are going to implement replica based approach. Here Optic disk is restricted by the Localized Principal Component Analysis (LPCA) and its shape is detected by a Customized Dynamic Shape Model (CDSM). The extraction of exudates fluid is done by mutual region growing and edge recognition methods. A digital fundus image coordinate system is built to present an enhanced depiction of the features. The success of the LPCA and CDSM algorithms can be attributed to the utilization of the Replica-Based methods. Performance of the replica based approach is measured in terms of optic disk boundary detection, sensitivity and specificity.